Benoit E. (1983). Syst'emes lents-rapides dans r3 et leur canards. Asterisque. 109-110
Brons M, Kaper TJ, Rotstein HG. (2008). Introduction to focus issue: mixed mode oscillations: experiment, computation, and analysis. Chaos (Woodbury, N.Y.). 18 [PubMed]
Desroches M, Krauskopf B, Osinga HM. (2008). Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh-Nagumo system. Chaos (Woodbury, N.Y.). 18 [PubMed]
Erchova I, McGonigle DJ. (2008). Rhythms of the brain: an examination of mixed mode oscillation approaches to the analysis of neurophysiological data. Chaos (Woodbury, N.Y.). 18 [PubMed]
Ermentrout B, Rubin J, Drover J, Su J. (2005). Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies SIAM J Appl Math. 65
Ermentrout GB. (2002). Simulating, Analyzing, and Animating Dynamical System: A Guide to XPPAUT for Researchers and Students Society for Industrial and Applied Mathematics (SIAM).
Ermentrout GB, Wechselberger M. (2009). Canards, clusters and synchronization in a weakly coupled interneuron model Siam Journal On Applied Dynamical Systems. 8
Fenichel N. (1979). Geometric singular perturbation theory for ordinary differential equations J Diff Eqn. 31
Guckenheimer J. (2008). Singular Hopf bifurcation in systems with two slow variables Siam Journal On Applied Dynamical Systems. 7
Guckenheimer J, Harris-Warrick R, Peck J, Willms A. (1997). Bifurcation, bursting, and spike frequency adaptation. Journal of computational neuroscience. 4 [PubMed]
Jones CKRT. (1995). Geometric singular perturbation theory Dynamical Systems Lecture Notes in Math.. 1609
Kinard TA, de Vries G, Sherman A, Satin LS. (1999). Modulation of the bursting properties of single mouse pancreatic beta-cells by artificial conductances. Biophysical journal. 76 [PubMed]
Kopell N, Wechselberger M, Rotstein H. (2008). Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model Siam Journal Of Dynamic Systems. 7
Krupa M, Popović N, Kopell N, Rotstein HG. (2008). Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron. Chaos (Woodbury, N.Y.). 18 [PubMed]
Kuryshev YA, Childs GV, Ritchie AK. (1996). Corticotropin-releasing hormone stimulates Ca2+ entry through L- and P-type Ca2+ channels in rat corticotropes. Endocrinology. 137 [PubMed]
LeBeau AP, Robson AB, McKinnon AE, Sneyd J. (1998). Analysis of a reduced model of corticotroph action potentials. Journal of theoretical biology. 192 [PubMed]
Morris C, Lecar H. (1981). Voltage oscillations in the barnacle giant muscle fiber. Biophysical journal. 35 [PubMed]
Rinzel J. (1987). A formal classification of bursting mechanisms in excitable systems. Mathematical Topics in Population Biology, Morphogenesis, and Neurosciences.. 71
Rinzel J, Ermentrout B. (1998). Analysis of neural excitability and oscillations. Methods In Neuronal Modeling 2nd Edition.
Rubin J, Wechselberger M. (2007). Giant squid-hidden canard: the 3D geometry of the Hodgkin-Huxley model. Biological cybernetics. 97 [PubMed]
Shorten PR, Robson AB, McKinnon AE, Wall DJ. (2000). CRH-induced electrical activity and calcium signalling in pituitary corticotrophs. Journal of theoretical biology. 206 [PubMed]
Stern JV, Osinga HM, LeBeau A, Sherman A. (2008). Resetting behavior in a model of bursting in secretory pituitary cells: distinguishing plateaus from pseudo-plateaus. Bulletin of mathematical biology. 70 [PubMed]
Szmolyan P, Wechselberger M. (2001). Canards in 3 J Diff Eqn. 177
Szmolyan P, Wechselberger M. (2004). Relaxation oscillations in R3 Journal Of Differential Equations. 200
Tabak J, Toporikova N, Freeman ME, Bertram R. (2007). Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents. Journal of computational neuroscience. 22 [PubMed]
Toporikova N, Tabak J, Freeman ME, Bertram R. (2008). A-type K(+) current can act as a trigger for bursting in the absence of a slow variable. Neural computation. 20 [PubMed]
Tsaneva-Atanasova K, Sherman A, van Goor F, Stojilkovic SS. (2007). Mechanism of spontaneous and receptor-controlled electrical activity in pituitary somatotrophs: experiments and theory. Journal of neurophysiology. 98 [PubMed]
Van Goor F, Zivadinovic D, Martinez-Fuentes AJ, Stojilkovic SS. (2001). Dependence of pituitary hormone secretion on the pattern of spontaneous voltage-gated calcium influx. Cell type-specific action potential secretion coupling. The Journal of biological chemistry. 276 [PubMed]
Wechselberger M. (2005). Existence and bifurcation of canards in 3 in the case of a folded node SIAM J Appl Dynam Sys. 4
Wechselberger M, Brons M, Krupa M. (2006). Mixed mode oscillations due to the generalized canard phenomenon Fields Institute Communications. 49
Wechselberger M, Krupa M. (2010). Local analysis near a folded saddle-node singularity Journal of Differential Equations. 248(12)
Zhang M, Goforth P, Bertram R, Sherman A, Satin L. (2003). The Ca2+ dynamics of isolated mouse beta-cells and islets: implications for mathematical models. Biophysical journal. 84 [PubMed]
Teka W, Tabak J, Bertram R. (2012). The relationship between two fast/slow analysis techniques for bursting oscillations. Chaos (Woodbury, N.Y.). 22 [PubMed]
Teka W, Tabak J, Vo T, Wechselberger M, Bertram R. (2011). The dynamics underlying pseudo-plateau bursting in a pituitary cell model. Journal of mathematical neuroscience. 1 [PubMed]
Vo T, Tabak J, Bertram R, Wechselberger M. (2014). A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells. Journal of computational neuroscience. 36 [PubMed]